Solution to: Stacking Coins
The maximal distance between the center of the topmost coin and the center of the lowermost coin is infinite!
To be precise, for N+1 coins the distance is d/2×(1+1/2+1/3+...+1/N). This sum approaches infinity when N approaches infinity. The idea is that you build up the stack from top to bottom, and places the edge of each next coin below the center of gravity of the coins above. In practice, one should take this infinity with a pinch of salt... Let us take for example the euro, with a diameter of 2.325 cm and a thickness of 2.125 mm. When you start stacking on your desk, then at the ceiling you have a distance of approximately 1 decimeter, at airplane height approximately 2 decimeters and at the moon approximately 3 decimeters! There is a scientific publication about this problem: "Leaning Tower of Lire", P.R. Johnson, American Journal of Physics 23, 240 (1955).